The number of jackets sold per week at a boutique shop is shown in the table, with the corresponding probabilities. Find mean, variance, and standard deviation of the distribution.

Number of jackets:   19          15           18          12          16
Probability P(X):        0.24        0.36       0.11       0.10       0.20

If the manager of the boutique shop wants to be sure that he has enough jackets for the next month, how many should the manager purchase?